This is talk 23 (of 31) at the Conference on Brain Network Dynamics
held at the University of California at Berkeley on January 26-27, 2007. Speaker is Robert Kozma, Division of Computer Science Department of Mathematical Sciences The University of Memphis, Memphis, TN 38152. http://www.cs.memphis.edu/~rkozma/
Recent experiments indicate the presence of frequent abrupt changes in brain dynamics covering large parts of each cerebral hemisphere. These large-scale oscillations show a characteristic frequency in the theta temporal band and plenty there is ample of evidence showing that they are markers of the subject's cognitive activity. We have introduced neuropercolation models as a mathematical framework to describe phase transitions in the cortex. Neuropercolation is a generalization of cellular automata, Hopfield memory arrays, and Conway's game of life, by merging the concepts of random graph theory and non-local interactions represented by axonal connections. Random noise plays a central role in the model, which is rooted in the pioneering work of Erdos and Renyi. We have indicated several key factors which determine phase transitions in our cortical model, including endogenously generated noise, the structure of the connectivity of neural populations with or without small-world effects, and the sparseness of the interactions between excitatory and inhibitory neural populations. Unlike phase transitions in physical systems, cortical phase transitions progress through metastable states, which have an intermittent character. The role of external input is described through stabilization of spatial patterns of amplitude modulation oscillations of the gamma carrier wave.